The cooling system is built oversized for any reasonable condition so that when it is compromised by some debris in the fins or some corrosion in the tubes it will still be able to function adequately. There is, of course, a limit to what it can do. If things get really plugged up there is no way it can cool properly.
So far you have done some good things but people have suggested more that can be done and you need to trust what they say. Those things include:
Check the contents of the trans pan. This should be the next step because what you find could alert you to pending disaster or it may prove that you don't have a real problem.
Scan the temp sensor when the truck is cold. It should read very close to ambient temperature. If it doesn't then while the pan is off replace the temp sensor. There is only one so what ever is reading temp is getting the info from the same place as everything else.
I agree that 240 is high but it isn't high enough to kill the transmission, yet. The thing is, if the sensor in the pan is reading 240 then it may be more than 300 coming out of the converter. That would be a real problem.
Just as a maintenance item, remove the cooling stack and clean it. It's a big project and will cost some money to replace the coolant but you don't need to discharge the A/C necessarily. While you are at it either take the radiator to a shop to get it cleaned out, run some flush through it or replace it. You can get a new radiator from RockAuto for $2-300. That isn't cheap but it beats the price of a trans by a long shot. You can plug up a cooling stack in about 15 minutes of driving through 3 foot tall weeds so it would not be surprising at all if that is your real problem.
While doing the the cooling stack thing it would be a good time to do the thermostats while you are in there with everything out of the way. I don't see any real problem with them but it is a normal maintenance thing to do on an older engine.
If you don't replace the radiator or take it to a shop to have it flushed, then be sure to flush the trans cooler both directions while it is out. I mean both of them, the radiator one and the separate one. I think if they were in bad shape you would have bigger problems than you do but it's worth the extra 15 minutes to do it. You can buy flush specifically intended for cleaning out the trans cooler at a parts store but you can also do a pretty good job with a garden sprayer full of strong soapy water followed by clean water followed by air. I would even follow that with some brake clean and air again but not everyone would agree with that.
I think you have already done enough to verify that your trans isn't slipping so I don't think you need to worry.
As far as fluid, there are really only a hand full of things that are critical. The fluid has to be compatible with the seals and friction materials it was built with. It has to be of the proper viscosity but there aren't a lot of options there so what you already have is probably good that way. All modern ATF formulas have a lot of detergent in them but it might be possible to find some that didn't. Dex 6 is really good on that account.
It used to be that rebuild shops used Mercon as a universal trans fluid because it has more friction modifiers in it than old Dexron so a lot of old GM transmissions used to run around with Ford fluid in them. Today it seem that everyone wants you to use their specific fluid or they promise death and destruction. I'm not sure I believe all of that but I try to stick with the recommendations as closely as I can. When it was recommended to you that you use ATF +4, as has been said, that is a Chrysler specification. Most +4 is full synthetic, like Dex 6. However the specifics are a little different. I would advise that you do exactly what the people who built the trans say to do. It is no longer an Allison or GM transmission, exactly. So what Allison or GM say no longer applies.
When the Allison 1000 transmission was first designed it was intended for use in smaller commercial trucks like wreckers and delivery vans. It was way more than a pickup needed. Pickup drivers want their trucks to drive like cars so a big beefy Allison would have been too harsh. Just think of how bus transmissions lurch when they shift. To make the Allison 1000 suitable for use in pickups they removed some of the friction materials by making some of the clutch plates with material on only one side instead of two.
This meant that there was less to rub together when the clutch was not applied and was slipping. That means less heat. Of course when they make the Allison 1000 tough again for hotrodding they put in plates with two sided frictions and set it up a little tighter than it used to be. The result is more rubbing and therefore more heat. That also means that there is more drag so that most trucks with "built" transmissions don't get the economy they used to. There's always a trade off.
Your cooling system is capable of handling the extra heat of a built trans but it has to be in good shape. What might work for a stock trans might not work for a built one.
